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Prove that there exist four points A, B, C, D (22)

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October 29, 2010
conicsparabolageometrygeometric transformationreflectiontrapezoidsymmetry

Problem Statement

A circle centered at a point FF and a parabola with focus FF have two common points. Prove that there exist four points A,B,C,DA, B, C, D on the circle such that the lines AB,BC,CDAB, BC, CD and DADA touch the parabola.
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